The field of data communications typically uses a modem to convey information from one location to another. Digital Subscriber Line (DSL) technology now enables modems to communicate large amounts of data. Modems communicate by modulating a baseband signal carrying digital data, converting the modulated digital data signal to an analog signal, and transmitting the analog signal over a conventional copper wire pair using techniques that are known in the art. These known techniques include mapping the information to be transmitted into a multidimensional signal space constellation. In some instances, a onedimensional signal space constellation can be employed, such as in the case of pulse amplitude modulation (PAM). The constellation can include both analog and digital information or only digital information.
In the above mentioned communications system, typically both digital data and an analog signal are to be transmitted. The data signal to be transmitted is represented by a sequence of data symbols, where each data symbol is associated with a particular N-dimensional signal point value taken from a signal space. Similarly, the analog signal, which for example can be represented by a voice signal, is processed so that it is mapped into the N-dimensional signal space to provide a voice signal point. This voice signal point defines the magnitude and angle of a voice signal vector about the origin of the signal space. The data symbol and the voice vector are then added together to select a resultant N-dimensional signal point. These N-dimensional signal points are grouped into signal space constellations and then transmitted to a far-end modem.
Upon reception of the transmitted N-dimensional signal point, the receiver of the far-end modem detects the embedded data symbol and subtracts the data symbol from the received N-dimensional signal point to yield the voice signal vector. This voice signal vector is then used to recreate the voice signal.
Square signal space constellations typically have a higher peak factor, and typically require more power to transmit a given amount of information than circular constellations. Square constellations also have a greater susceptibility to harmonic distortion. For example, in a 256 point two dimensional circular constellation, the constellation point, or symbol, with the highest power has the x, y coordinates 17, 5 with a peak power of 17.sup.2 +5.sup.2 =314, whereas the highest power point in a square constellation has the x, y coordinates 15, 15 with a peak power of 15.sup.2 +15.sup.2 =450. As can be seen, the peak power of a circular constellation is 1.6 dB lower than that of a square constellation.
In the above mentioned communications system it would be beneficial to allow the transmission of additional special marker symbols in a signal space constellation. These special markers can be used to convey a number of command and control functions from one communication device to another. Square constellations encode exactly N-bits in a constellation with 2.sup.N points. This eliminates the possibility of transmitting any additional special marker symbols. Therefore a need exists for the ability to transmit additional special marker symbols in a signal space constellation.